Main Discussion Area > Arrows
arrow spine
blindarcher:
Hi All. I struggle with the concept of dynamic arrow spine. The following are thoughts I have that may be correct or incorrect, so feedback is more than welcome. I just have trouble putting all the pieces together:
1. The arrow itself has a natural frequency, depending on distance between end conditions (e.g. draw length defined by arrow nock point and handle).
2. I struggle with what those end conditions really are, such as pinned-free, free-free, pinned with lateral spring constant-free, etc.?
3. I imagine that as the string rolls off the fingers, there is a lateral displacement of the string adding elastic energy to the system in addition to the arrow stiffness as well as a displacement constraint. How important is this? Should I be thinking of a bow/arrow system lateral frequency and not just arrow?
4. I imagine the arrowhead may affect the natural frequency of the arrow and maybe reduce it? How much does this contribute to the vibrational response relative to arrow stiffness?
5. If for instance the correct end conditions for the arrow is free-free, then I imagine that the frequency of vibration is independent of draw weight for given draw length. However, the amplitude of lateral displacement may be a function of draw weight, maybe?
6. So, whatever the correct means to characterize the arrow's frequency of vibration might be, it is my understanding that the period of vibration (1/frequency) should be in proper ratio with the time for the arrow to leave the bow after release to avoid the arrow backend from slapping the handle. The time for the arrow to leave the bow is a function of bow stored energy (area under static force/draw curve), bow efficiency, arrow mass and draw length.
It is the method to characterize the arrow natural frequency that alludes me. Specifically, end conditions and how important are the mass of the arrowhead and lateral stiffness of the string?
Cheers!
Jon
willie:
Jon,
consider the arrow in flight and the forces acting on it after it has left the bow.
the fletching and the residual vibrations of the shaft left from the "launch".
I think the finger flip applied at the moment of max acceleration/axial compression is the biggest factor to consider before it leaves the string.
blindarcher:
Thanks Willie,
Actually, the fight of the arrow after it leaves the bow is the easy part for me. I can solve the equations of motion, including aerodynamics (requires aerodynamic and stability derivatives 3 DOF). Doing so allows me to understand the arrow's momentum with time and distance. It is characterizing the arrow's vibrational mode from release to when the nock end passes the handle; hence the setting up residual vibration as the arrow leaves the bow that you mentioned. My concern is matching the vibrational frequency and mode of the arrow/string system to the time it takes the arrow nock to travel the distance of the draw length. I do not want the arrow nock end to slap the handle. This is what I believe is what the dynamic spine is all about, I think.
Thanks again and cheers!
willie:
--- Quote ---It is characterizing the arrow's vibrational mode from release to when the nock end passes the handle; hence the setting up residual vibration as the arrow leaves the bow that you mentioned. My concern is matching the vibrational frequency and mode of the arrow/string system to the time it takes the arrow nock to travel the distance of the draw length.
--- End quote ---
I can't say I have go so far as to work the math for a particular arrow, but I do recall a chapter in a text where (in theory), a column (arrow) in static compression was compared to an arrow under acceleration. It seemed the arrow undergoing acceleration needed to be of a larger diameter towards the nock end. Of course that is the same area where we often taper the arrow most to help the recovery from the lateral finger flip. I could probably find that pdf if you pm your email.
blindarcher:
Thanks Willie,
Jon
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